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Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient…

Fair representation learning is an attractive approach that promises fairness of downstream predictors by encoding sensitive data. Unfortunately, recent work has shown that strong adversarial predictors can still exhibit unfairness by…

We introduce the notion of Fermi flow for hypersurfaces in Riemannian manifolds. It turns out that this is a powerful tool to study the geometry of distance surfaces about a given initial hypersurface. Some of the results in this paper are…

In this work we explore the advantages of end-to-end learning of multilayer maps offered by feed forward neural-networks (FFNN) for learning and predicting dynamics from transient fluid flow data.While machine learning in general depends on…

Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…

Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in…

Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly…

Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in…

We propose a federated methodology to learn low-dimensional representations from a dataset that is distributed among several clients. In particular, we move away from the commonly-used cross-entropy loss in federated learning, and seek to…

State-of-the-art image segmentation algorithms generally consist of at least two successive and distinct computations: a boundary detection process that uses local image information to classify image locations as boundaries between objects,…

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…

We present a new paradigm for creating random features to approximate bi-variate functions (in particular, kernels) defined on general manifolds. This new mechanism of Manifold Random Features (MRFs) leverages discretization of the manifold…

Natural data observed in $\mathbb{R}^n$ is often constrained to an $m$-dimensional manifold $\mathcal{M}$, where $m < n$. This work focuses on the task of building theoretically principled generative models for such data. Current generative…

Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for…

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input…

Diffusion models can learn rich representations during data generation, showing potential for Self-Supervised Learning (SSL), but they face a trade-off between generative quality and discriminative performance. Their iterative sampling also…

We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…

Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to…

Clustering on the data with multiple aspects, such as multi-view or multi-type relational data, has become popular in recent years due to their wide applicability. The approach using manifold learning with the Non-negative Matrix…

Diffusion probabilistic models have quickly become a major approach for generative modeling of images, 3D geometry, video and other domains. However, to adapt diffusion generative modeling to these domains the denoising network needs to be…